Mokp'o Things to Do
In my opinion, Yudal Beach is only worthy of a short visit. It is small and rather unimpressive. But on a hot day, there are a few nice vistas and cafes that sell ice cream to help beat the heat.
There is a large outdoor public pool that will cater to most locals just south of the main beach area.
Between the city center and Yudal Beach, is Yudal-san (Yudal mountain). It has several hiking trails, but you can start either by the city or just behind the public pool and finish at the opposite one. Hike time for the entire circuit may be ~1.5 hours total.
The mountain is not tall, but does offer some nice view both of the sea and the city. Along the highest spiny ridge, there are a few small observation pavilions which could also serve as a picnic/rest area. Near to the top are also some old Buddhist carvings in the rock faces.